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Question
In a school there are 1000 students, out of which 430 are girls. It is known that out of 430, 10% of the girls study in class XII. What is the probability that a student chosen randomly studies in class XII given that the chosen student is a girl?
Solution
\[\text{ Suppose S represents a student chosen randomly studying in class XII and G represents a female student chosen randomly } . \]
\[\text{ We have, } \]
\[P\left( G \right) = \frac{430}{1000} \]
\[P\left( S/G \right) = \frac{43}{1000}\]
\[\text{ Now } , \]
\[P\left( S/G \right) = \frac{P\left( S \cap G \right)}{P\left( G \right)} = \frac{\frac{43}{1000}}{\frac{430}{1000}} = \frac{1}{10}\]
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